Answer:
Hypotenuse² = Base² + Altitude²
35² = 15² + x²
1225 = 225 + x²
x² = 1225 - 225
x² = 1000
<u>X = 10√10</u>
Answer:
By using hypothesis test at α = 0.01, we cannot conclude that the proportion of high school teachers who were single greater than the proportion of elementary teachers who were single
Step-by-step explanation:
let p1 be the proportion of elementary teachers who were single
let p2 be the proportion of high school teachers who were single
Then, the null and alternative hypotheses are:
: p2=p1
: p2>p1
We need to calculate the test statistic of the sample proportion for elementary teachers who were single.
It can be calculated as follows:
where
- p(s) is the sample proportion of high school teachers who were single (
) - p is the proportion of elementary teachers who were single (
)
- N is the sample size (180)
Using the numbers, we get
≈ 1.88
Using z-table, corresponding P-Value is ≈0.03
Since 0.03>0.01 we fail to reject the null hypothesis. (The result is not significant at α = 0.01)
Answer:
so you're going to need to find the slope. in order to do that use (y2-y1)/(x2-x1)
(7-(-2))/(0-8)
simplify
9/-8
simplify -9/8
now using y=mx+b, we need to find b. so we can plug in the coordinates of (0,7) or (8,-2). let's use (8,-2) because it involves more math.
y=mx+b
-2=(-9/8)(8)+b
multiply (-9/8) by 8 to get -9
-2=-9+b
add 9 to both sides
7=b
so our equation is now
y=-(9/8)x+7
Step-by-step explanation:
Answer:
4 hours
Step-by-step explanation:
For three visits, the electrician earned $40 × 3 = $120 in "per-visit" charges. For working x hours, he earned 20x in "per-hour" charges. The total of these came to 50x:
120 +20x = 50x
120 = 30x . . . . . . . . subtract 20x
4 = x . . . . . . . . . . . . . divide by 30
The electrician worked 4 hours that day.
Answer:
No, the maximum height that the balloon can reach is 9ft.
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
The function h(x) =-0.5(x-4)² +9, is a Quadratic Function in the Vertex form.
Vertex form: f (x) = a(x - h) 2 + k
Where:
- (h, k) is the vertex of the parabola-
- h is the horizontal shift (how far left, or right, the graph has shifted from x = 0).
- k represents the vertical shift (how far up, or down, the graph has shifted from y = 0).
In this case a = -0.5, it means that the parabola opens downward and has a maximum point at the vertex.
So, the maximum height that the balloon can reach is k=9ft.
9 ∠ 12
The balloon will not hit the ceiling 12 ft above the pool.
Feel free to ask for more if needed or if you did not understand something.
